# Mathematical Sciences Research Institute

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# Summer Graduate School

A Window into Zeta and Modular Physics June 16, 2008 - June 27, 2008
Organizers Floyd Williams (University of Massachusetts) and Klaus Kirsten (Baylor University)
Lecturer(s) No Lecturers Assigned Yet.
Speaker(s)

## Show List of Speakers

Description Speaker list :Klaus Kirsten (co-organizer, Baylor University), Geoffrey Mason (UCSC), Audrey Terras (UCSD), Michael Tuite (National University of Ireland), and Floyd Williams (organizer,University of Massachusetts). In recent years,a noteworthy and very fruitful interlacing of number theory and physics has emerged. As indicated in the September 2007 issue of the AMS Notices, for example, a new journal "Communications in Number Theory and Physics" has just been launched to follow significant interactions and dynamics between these two fields. Several books are now available, in addition to an array of conference and workshop activity, that accent this fortunate merger of "pure" mathematics and physical theory-with applications that range from field theory (conformal and topological), extended objects (strings and branes) cosmology and black hole physics, to Bose-Einstein condensation and the theory of relativistic gases. The workshop is designed to provide students a bridge, or a window, into this vast, interesting, rapidly-developing, interactive arena. Some special attention would be given to zeta and modular aspects of the interactions. The students would be provided with some lecture notes and hand-outs, and with very ample opportunities to engage in discussion/question sessions with the lecturers, apart from the two hours per day lectures.In some cases, web material will be available prior to the workshop-all in a concerted effort to afford maximal learning situations. Prof.Terras, for example, already has some introductory notes on line to help students get a head start towards her lectures on quantum chaos: http://www.math.ucsd.edu/~aterras/newchaos.pdf; also compare http://www.math.ucsd.edu/~aterras/newbook.pdf The students would be required to have a good working knowledge of complex variables,including familiarity with infinite products and the gamma function.It is suggested they should read some introductory material on the Riemannn zeta function ( say, from a text on complex variables), and it would be helpful for them to do some minimal reading on the Dedekind eta functions. The material in Tom Apostol's Springer Graduate Text on "Modular Functions and Dirichlet Series in Number Theory" (chapter 3) , for example, is more than needed for a basic understanding of the Dedekind eta function. Alternately, one can obtain the same information on zeta and eta (without proofs) by simply going to Google. The organizer has emphasized, repeatedly, to the speakers that our aim is to keep the lectures elementary, expository, and self-contained as possible. Vertex Operators (PDF 165KB) Modular Forms in Vertex Operator Algebras (PDF 228KB) Audrey Terras - Lecture 1 (PDF 1.27MB) Audrey Terras - Lecture 2 (PDF 860KB) Audrey Terras - Lecture 3 (PDF 1.91MB) First week : Monday: Riemann zeta function(analytic continuation,special values,and infinity factorial as a simple example of zeta regularization)/Floyd/ introduction to Hurewitz,Epstein,Barnes zeta/Klaus Tuesday: A simple example of a Casimir enengy calculation(another example of zeta regularization)/Klaus/introduction to Selberg,Ihara,Ruelle zeta/Audrey Wednesday: conformal field theory (CFT) for beginners/Geoff and Michael/ modular forms of positive weight and their Fourier coefficients/Floyd Thursday: zeta zeros/poles and distribution of primes/Audrey/CFT/Geoff and Michael Friday: Dedekind eta and its reciprocal with some string theory remarks/Floyd/computation of functional determinants via contour integrals/Klaus Second week Monday: polylog expansion of a partition function with some intuitive remarks on Bose-Einstein condensation/Klaus/application of Epstein-Barnes zeta to gravity in extra dimensions/Floyd Tuesday: modular forms of negative weight (more on the reciprocal of the Dedekind eta function,and a statement of the Rademacher-Zuckerman formula for Fourier coefficients)/Floyd/CFT/Geoff and Michael Wednesday: quantum chaos (some applications of Audrey's earlier lectures)/Audrey/CFT/Geoff and Michael Thursday: generalized Cardy formula for black hole entropy(applications of forms of non-positive weight)/Floyd/unscheduled time for review,miscellaneous material,extra time for speakers,etc. Friday: unscheduled time Photo of workshop participants (.98MB)

Funding & Logistics

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MSRI has preferred rates at the Rose Garden Inn, depending on room availability. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show the MSRI rate on all room types available.

MSRI has preferred rates at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability. MSRI has preferred rates of$149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and click Book Now. Once on the reservation page, click “Promo/Corporate Code“ and input the code: msri. MSRI has preferred rates of$110 - \$140 at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select “I am an individual traveler affiliated with MSRI”.

Additional lodging options may be found on our short term housing page.

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Schedule
Jun 16, 2008
Monday
 09:30 AM - 10:30 AM Riemann's zeta function Floyd Williams 11:00 AM - 12:00 PM Introduction to Hurewitz,Epstein,Barnes zeta Klaus Kirsten (Baylor University)
Jun 17, 2008
Tuesday
 09:30 AM - 10:30 AM Conformal field theory (CFT) for beginners Geoff Mason (University of California, Santa Cruz) 11:00 AM - 12:00 PM A simple example of a Casimir enengy calculation(another example of zeta regularization) Klaus Kirsten (Baylor University)
Jun 18, 2008
Wednesday
 09:30 AM - 10:30 AM Modular forms of positive weight and their Fourier coefficients Floyd Williams 11:00 AM - 12:00 PM Conformal field theory (CFT) Geoff Mason (University of California, Santa Cruz)
Jun 19, 2008
Thursday
 09:30 AM - 10:30 AM Introduction to Selberg,Ihara,Ruelle zeta Audrey Terras 11:00 AM - 12:00 PM zeta zeros/poles and distribution of primes Audrey Terras
Jun 20, 2008
Friday
 09:30 AM - 10:30 AM Dedekind eta and its reciprocal with some string theory remarks Floyd Williams 11:00 AM - 12:00 PM Computation of functional determinants via contour integrals Klaus Kirsten (Baylor University)
Jun 23, 2008
Monday
 09:30 AM - 10:30 AM Polylog expansion of a partition function with some intuitive remarks on Bose-Einstein condensation Klaus Kirsten (Baylor University) 11:00 AM - 12:00 PM Quantum chaos Audrey Terras
Jun 24, 2008
Tuesday
 09:30 AM - 10:30 AM Modular forms of negative weight (more on the reciprocal of the Dedekind eta function,and a statement of the Rademacher-Zuckerman formula for Fourier coefficients) Floyd Williams 11:00 AM - 12:00 PM CFT Geoff Mason (University of California, Santa Cruz)
Jun 25, 2008
Wednesday
 09:30 AM - 10:30 AM A Window into Zeta an Modular Physics talk I Michael Tuite 11:00 AM - 12:00 PM A Window into Zeta an Modular Physics talk II Michael Tuite
Jun 26, 2008
Thursday
 09:30 AM - 10:30 AM Generalized Cardy formula for black hole entropy(applications of forms of non-positive weight) Floyd Williams 11:00 AM - 12:00 PM On Relating d-dimensional FRLW Cosmology to Bose-Einstein Condensates Jennie D'Ambroise
Jun 27, 2008
Friday
 09:30 AM - 10:15 AM Zeta and L-functions Paul Nelson 10:30 AM - 11:15 AM Arithmetic of String Compactification and Emergent Spacetime. Savan Kharel 11:15 AM - 12:00 PM How a soliton Illuminates a Blackhole Shabnam Beheshti (Rutgers University)